TAS5518 datasheet(24/103 Pages) TI

24 / 103 page

Introduction

SLES115 — August 2004

TAS5518

1.5.2.1

28-Bit 5.23 Number Format

All mixer gain coefficients are 28-bit coefficients using a 5.23 number format. Numbers formatted as 5.23

numbers means that there are 5 bits to the left of the decimal point and 23 bits to the right of the decimal point.

This is shown in the Figure 1−7.

2−23 Bit

S_xxxx.xxxx_xxxx_xxxx_xxxx_xxx

2−4 Bit

2−1 Bit

20 Bit

Sign Bit

23 Bit

Figure 1−7. 5.23 Format

The decimal value of a 5.23 format number can be found by following the weighting shown in Figure 1−8. If

the most significant bit is logic 0, the number is a positive number, and the weighting shown yields the correct

number. If the most significant bit is a logic 1, then the number is a negative number. In this case every bit must

be inverted, a 1 added to the result, and then the weighting shown in Figure 1−8 applied to obtain the

magnitude of the negative number.

(1 or 0) x 23 + (1 or 0) x 22 + … + (1 or 0) x 20 + (1 or 0) x 2−1 + … + (1 or 0) x 2−4 + … + (1 or 0) x 2−23

23 Bit

22 Bit

20 Bit

2−1 Bit

2−4 Bit

2−23 Bit

Figure 1−8. Conversion Weighting Factors—5.23 Format to Floating Point

Gain coefficients, entered via the I2C bus, must be entered as 32-bit binary numbers. The format of the 32-bit

number (4-byte or 8-digit hexadecimal number) is shown in Figure 1−9.

Coefficient

Digit 8

u u u

S x x x

Coefficient

Digit 7

x. x x x

Coefficient

Digit 6

x x x x

Coefficient

Digit 5

x x x x

Coefficient

Digit 4

x x x x

Coefficient

Digit 3

x x x x

Coefficient

Digit 2

x x x x

Coefficient

Digit 1

Fraction

Digit 5

Sign

Bit

Fraction

Digit 6

Fraction

Digit 4

Fraction

Digit 3

Fraction

Digit 2

Fraction

Digit 1

Integer

Digit 1

u = unused or don’t care bits

Digit = hexadecimal digit

Figure 1−9. Alignment of 5.23 Coefficient in 32-Bit I2C Word

As Figure 1−9 shows, the hex value of the integer part of the gain coefficient cannot be concatenated with the

hex value of the fractional part of the gain coefficient to form the 32-bit I2C coefficient. The reason is that the

28-bit coefficient contains 5 bits of integer, and thus the integer part of the coefficient occupies all of one hex

digit and the most significant bit of the second hex digit. In the same way, the fractional part occupies the lower

3 bits of the second hex digit, and then occupies the other five hex digits (with the eighth digit being the

zero-valued most significant hex digit).

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